Communications of the ACM - Special issue on parallelism
Algorithms for computer algebra
Algorithms for computer algebra
Displacement structure: theory and applications
SIAM Review
A Fast Stable Solver for Nonsymmetric Toeplitz and Quasi-Toeplitz Systems of Linear Equations
SIAM Journal on Matrix Analysis and Applications
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
Distributed Symbolic Computation with DTS
IRREGULAR '95 Proceedings of the Second International Workshop on Parallel Algorithms for Irregularly Structured Problems
Parallel Computation of Modular Multivariate Polynominal Resultants on a Shared Memory Machine
CONPAR 94 - VAPP VI Proceedings of the Third Joint International Conference on Vector and Parallel Processing: Parallel Processing
A New Approach to Resultant Computations and Other Algorithms with Exact Division
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Probabilistic algorithms for computing resultants
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Efficient parallel factorization and solution of structured and unstructured linear systems
Journal of Computer and System Sciences
A complete modular resultant algorithm targeted for realization on graphics hardware
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Modular resultant algorithm for graphics processors
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
IEEE Transactions on Signal Processing
Arrangement computation for planar algebraic curves
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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In this article we report on our experience in computing resultants of bivariate polynomials on Graphics Processing Units (GPU). Following the outline of Collins' modular approach [6], our algorithm starts by mapping the input polynomials to a finite field for sufficiently many primes m. Next, the GPU algorithm evaluates the polynomials at a number of fixed points x@?Z"m, and computes a set of univariate resultants for each modular image. Afterwards, the resultant is reconstructed using polynomial interpolation and Chinese remaindering. The GPU returns resultant coefficients in the form of Mixed Radix (MR) digits. Finally, large integer coefficients are recovered from the MR representation on the CPU. All computations performed by the algorithm (except for, partly, Chinese remaindering) are outsourced to the graphics processor thereby minimizing the amount of work to be done on the host machine. The main theoretical contribution of this work is the modification of Collins' modular algorithm using the methods of matrix algebra to make an efficient realization on the GPU feasible. According to the benchmarks, our algorithm outperforms a CPU-based resultant algorithm from 64-bit Maple 14 by a factor of 100.